Unit vector perpendicular to i -2 j +2 k and lying in the plane containing i + j -2 k and - i +2 j + k is

Step-by-step solution

Let a = i -2 j + k , b = i + j -2 k and c =- i +2 j + k Now, b c = | array ccc i & j & k 1 & 1 & -2 -1 & 2 & 1 array |=5 i + j +3 k Now, a ( b c )= | array ccc i & j & k 1 & -2 & 2 5 & 1 & 3 array |=-8 i +7 j +11 k Now, any vector perpendicular to a and lying in the plane containing i + j -2 k and - i +2 j + k is (a (b c)) aligned Required unit vector &= (-8 i +7 j +11 k ) (-8)²+(7)²+(11)² &= (-8 i +7 j +11 k ) 234 aligned